The infimum, supremum and geodesic length of a braid conjugacy class

Algorithmic solutions to the conjugacy problem in the braid groups B_n were given by Elrifai-Morton in 1994 and by the authors in 1998. Both solutions yield two conjugacy class invariants which are known as `inf' and `sup'. A problem which was left unsolved in both papers was the number m of times one must `cycle' (resp. `decycle') in order to increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the given conjugacy class. Our main result is to prove that m is bounded above by n-2 in the situation of the second algorithm and by ((n^2-n)/2)-1 in the situation of the first. As a corollary, we show that the computation of inf and sup is polynomial in both word length and braid index, in both algorithms. The integers inf and sup determine (but are not determined by) the shortest geodesic length for elements in a conjugacy class, as defined by Charney, and so we also obtain a polynomial-time algorithm for computing this geodesic length.Comment: 15 pages. Journa

Topic congruence and topic interest: How do they affect second language reading comprehension?

Because human memory is largely reconstructive, people tend to reorganize and reevaluate an event in a way that is coherent to the truth values held in their belief system. This study investigated the role of topic congruence (defined as whether the reading content corresponds with readers’ prior beliefs towards a contentious topic) in second language (L2) reading comprehension. In addition to the main variable, topic congruence, the role of topic interest was also explored. Sixty Korean native readers in the US and Korea read two argumentative passages in English, one discussing the pros of voluntary euthanasia, the other presenting the cons. Quality analysis of immediate recall protocols, defined as relative amount of higher and lower levels of information units correctly remembered, was performed by a repeated-measures multivariate analysis of variance. The results showed that topic congruence and topic interest affected the L2 readers’ recall of lower-level textual information in complex ways

Instability Waves in the Gulf Stream Front and Its Thermocline Layer

Linear instability calculations were carried out on a three layer Gulf Stream front model in an attempt to elucidate the interaction of the thermocline layer with surface slopewater shoreward of the front. The basic state is geostrophic balance and constant potential vorticity in the two active layers, but the perturbations are ageostrophic. The flow is found to be unstable to long wave perturbations, the wavelength of the most unstable wave to be of order 10 radii of deformation. The instability is mainly baroclinic, 75-85% of the energy supply to the growing perturbation coming from basic flow potential energy. Calculated wavelengths and growth rates, using parameters typical of the Gulf Stream, are similar to those observed. The eigenfunctions and particle trajectories reveal large cross-frontal excursions in the thermocline layer, and a large, if weak, cyclonic eddy in the surface slopewater in a meander trough

Seasonal Variability of Heat and Mass Transport Process in the Upper Tropical Atlantic Ocean: A Numerical Model Study

A simple 2.5 layer numerical model was developed and used to illustrate the seasonal variability of heat and mass transports in the upper tropical Atlantic Ocean, associated with the seasonal movement of the Inter-Tropical Convergence Zone (ITCZ). The model ocean was forced by seasonally varying climatological wind and heat flux fields. The entrainment at the base of the mixed layer was scaled by wind stress and shear at the bottom of the mixed layer. On an annual average, the northward transport of the tropical warm water is about 11 Sv, with roughly 10 Sv associated with entrainment of upper thermocline water and the other 1 Sv executing a cross-equatorial path continuously from the South Atlantic. Out of the total 10 Sv of the needed upper thermocline water, 9 Sv enters the equatorial belt from the South Atlantic. The seasonal response to the ITCZ movement was most striking in the entrainment rate and the warm water escape rate across the northern edge of the equatorial cell. The entrainment rate was found to be significant during May/December and ceased between January and April. The locally forced equilibrium response between the interfacial shear and the zonal wind stress east of 30°W appears to be responsible for this cycle. The warm water escape toward the North Atlantic takes place mainly between December and May and stops during July/September. Further investigation suggested that the seasonal intensification of the North Equatorial Countercurrent (NECC) serves as a major obstacle to the warm water escape: during July/September the strong negative wind stress curl north of the equator intensifies the NECC, which requires a source of mass at its origin in the west. The North Brazil Current (NBC), therefore, veers offshore completely and provides the mass, terminating the warm water escape via the NBC-Guiana Current route. Strengthening of the NECC also steepens the mixed layer floor, forming a strong potential vorticity front along the northern edge of the NECC. The northward warm water escape via the eastern leg of the cyclonic gyre is therefore limited. In addition, the northward Ekman transport also reaches a minimum during this period. As a result of seasonal variations of the two key processes, namely the entrainment and the meridional transport across the northern edge of the equatorial cell, the tropical warm water pool experiences heat storage during May/October and heat escape in November/April. The heat budget study of the equatorial mixed layer revealed that, on an annual average, heat gain at the sea surface between 8°S and 8°N is about 0.35 PW, and is used exclusively to warm up the cold water entrained from the upper thermocline layer. The heat-anomaly fluxes across the zonal boundaries are negligibly small. Further analysis showed that the sea surface temperature variation in the tropical Atlantic Ocean is determined by the local heat balance between the atmospheric heating and the entrainment cooling. The model results suggested that the ITCZ movement is the primary cause of the net northward heat transport and its seasonal variation observed in the upper tropical Atlantic Ocean

Gyrotropic linear and nonlinear motions of a magnetic vortex in soft magnetic nanodots

The authors investigated the gyrotropic linear and nonlinear motions of a magnetic vortex in soft magnetic cylindrical nanodots under in-plane oscillating magnetic fields of different frequencies and amplitudes, by employing both micromagnetic simulations and the numerical solutions of Thiele's equation of motion [Phys. Rev. Lett. 30, 230 (1973)]. Not only noncircular elliptical vortex-core orbital trajectories in the linear regime but also complex trajectories including stadiumlike shape in the nonlinear regime were observed from the micromagnetic simulations and were in excellent agreement with the numerical solutions of the analytical equations of motion. It was verified that the numerical solutions of Thiele's equation are promisingly applicable in order to predict and describe well such complex vortex gyrotropic linear and nonlinear motions in both the initial transient and later steady states. These results enrich the fundamental understanding of the linear and nonlinear motions of vortices in confined magnetic elements in response to oscillating driving forces.open352

Instability waves in the Gulf Stream front and its thermocline layer

We carried out linear instability calculations on a three layer Gulf Stream front model in an attempt to elucidate the interaction of the thermocline layer with surface slopewater shoreward of the front. The basic state is geostrophic balance and constant potential vorticity in the two active layers, but the perturbations are ageostrophic. We found the flow to be unstable to long wave perturbations, the wavelength of the most unstable wave to be of the order of 10 radii of deformation. The instability is mainly baroclinic, 75–85% of the energy supply to the growing perturbation coming from basic flow potential energy. Calculated wavelengths, phase speeds and growth rates, using parameters typical of the Gulf Stream, are similar to those observed. The eigenfunctions of the perturbations show peak cross-front thermocline motions near the inflection points of a frontal wave, and a cyclonic eddy with closed streamlines under a trough, an anticyclonic eddy under a crest. The combined flow (basic state plus perturbation) in the thermocline layer follows the surface streamlines closely, except for small cross-stream anomalies, shoreward just upstream of a wave crest, seaward upstream of a trough. Calculated trajectories have characteristics similar to those observed by RAFOS floats, except that they suggest exchange of thermocline waters exclusively with slopewater

Warm Water Formation and Escape in the Upper Tropical Atlantic Ocean - 1. A Literature Review

We review current understanding of the warm water formation and escape process in the tropical Atlantic Ocean and point out the physical aspects of the process not yet fully explored. From this review, we found a need for a simple model capable of describing the first-order heat and mass balance in the tropical Atlantic Ocean. This line of work is continued in part 2 [Lee and Csanady, this issue]. Copyright 1999 by the American Geophysical Union

Warm Water Formation and Escape in the Upper Tropical Atlantic Ocean - 2. A Numerical Model Study

We seek the simplest mass and heat balance scenario within the upper tropical Atlantic Ocean using a 2.5-layer numerical model, with the help of a newly suggested entrainment formula. The model ocean is driven by the seasonal wind and heat flux associated with the movement of the Intertropical Convergence Zone (ITCZ). The entrainment rate is scaled by the product of wind stress and shear at the bottom of the mixed layer. On an annual average, the northward transport of the tropical warm water is about 11 Sv, with roughly 10 Sv associated with entrainment of upper thermocline water. Out of the total 10 Sv of the needed upper thermocline water, 9 Sv enters the equatorial cell from the South Atlantic. The seasonal response to the ITCZ movement is most striking in the entrainment rate and the northward warm water escape rate. The entrainment is significant during May/December and ceases between January and March. The locally forced equilibrium response between the interface shear and the zonal wind stress east of 30øW appears to be responsible for this cycle. The warm water escape toward the North Atlantic takes place mainly from October to June and nearly stops during July/September. As a result of seasonal variations of the two key processes, namely, the entrainment and the northward warm water escape, the tropical warm water pool stores heat during May/October and lets heat escape in November/April. Copyright 1999 by the American Geophysical Union

Remarkable enhancement of domain-wall velocity in magnetic nanostripes

Remarkable reductions in the velocity of magnetic-field (or electric current)-driven domain-wall (DW) motions in ferromagnetic nanostripes have typically been observed under magnetic fields stronger than the Walker threshold field [N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 (1974)]. This velocity breakdown is known to be associated with an oscillatory dynamic transformation between transverse- and antivortex (or vortex)-type DWs during their propagations. The authors propose, as the result of numerical calculations, a simple means to suppress the velocity breakdown and rather enhance the DW velocities, using a magnetic underlayer of strong perpendicular magnetic anisotropy. This underlayer plays a crucial role in preventing the nucleation of antivortex (or vortex)-type DWs at the edges of nanostripes, in the process of periodic dynamic transformations from the transverse into antivortex- or vortex-type wall. The present study not only offers a promising means of the speedup of DW propagations to levels required for their technological application to ultrafast information-storage or logic devices, but also provides insight into its underlying mechanism.open383